Roberto Serrano

The Theory of Implementation of Social Choice Rules

Suppose that the goals of a society can be summarized in a social choice rule, i.e., a mapping from relevant underlying parameters to final outcomes. Typically, the underlying parameters (e.g., individual preferences) are private information to the agents in society. The implementation problem is then formulated: under what circumstances can one design a mechanism so that the private information is truthfully elicited and the social optimum ends up being implemented? In designing such a mechanism, appropriate incentives will have to be given to the agents so that they do not wish to misrepresent their information. The theory of implementation or mechanism design formalizes this “social engineering” problem and provides answers to the question just posed. I survey the theory of implementation in this article, emphasizing the results based on two behavioral assumptions for the agents (dominant strategies and Nash equilibrium). Examples discussed include voting, and the allocation of private and public goods under complete and incomplete information.

Fifty years of the nash program,1953-2003

This paper is a survey of the work in the Nash program for coalitional games, a research agenda proposed by Nash (1953) to bridge the gap between the non-cooperative and cooperative approaches to game theory.

A Decentralized Market with Common Values Uncertainty: Non-Steady States

We analyse a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and efficiency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is two-sided or one-sided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steadystate equilibria of a model where agents enter the market every period.

Agenda Restrictions in Multi-Issue Bargaining

Abstract We study a bilateral multi-issue bargaining procedure with complete information and endogenous agenda. In the procedure, proposals must be made on only one issue at a time, although the proposer can choose which issue to bring to the table. When bargaining frictions are small, there is a large multiplicity of equilibrium agreements, including ones with delay. However, equilibrium payoffs cannot be made arbitrarily small—perpetual disagreement cannot be supported in equilibrium. This multiplicity contrasts with the uniqueness found in the literature for a procedure where offers can be made in any subset of remaining issues.

Multiplicity of Mixed Equilibria in Mechanisms: A Unified Approach to Exact and Approximate Implementation

We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.

On Watson's Non-Forcing Contracts and Renegotiation

Watson (2002) proposes non-forcing contracts as a way to show the limitations of the mechanism design program with ex-post renegotiation (Maskin and Moore (1999)). If one takes a partial implementation approach, as Watson does, we show that non-forcing contracts do not constitute an intermediate paradigm between implementation with no renegotiation and with ex-post renegotiation. Moreover, taking a full implementation approach, non-forcing contracts fail if and only if one goes outside of the constraints identified by Maskin and Moore, because of the appearance of undesirable equilibria.

Decentralized Information and the Walrasian Outcome: A Pairwise Meetings Market with Private Values

Abstract I study a one-time entry market for a single indivisible good, where buyers and sellers, privately informed regarding their valuation for the good, are randomly matched, bargain, and in the event of agreement, trade and exit the market. Each agent’s search procedure is modeled as a sequence of discrete double auctions. For each value of the discount factor, the equilibrium behavior of traders satisfies a certain property of monotonicity within each side of the market—the lower a trader’s potential surplus the tougher his market position. As discounting is removed, equilibria with Walrasian and non-Walrasian features persist, although sufficient conditions are identified to single out the Walrasian outcome.

Equilibrium Blocking in Large Quasilinear Economies

We study information transmission in large interim quasilinear economies using the theory of the core. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, because blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We focus on independent replicas of the basic economy. We offer both negative and positive convergence results as a function of the complexity of the mechanisms used by coalitions. Furthermore, all of the results are robust to the relaxation of the incentive constraints. Results for ex post and signal-based replica processes are also obtained.

Strategic bargaining, surplus sharing problems and the nucleolus

Abstract Suppose that n agents are trying to reach an agreement on how to split an estate over which they have claims. They do so through decentralized negotiations instead of appealing to an arbitrator. In this context, I study a consistency-based multilateral bargaining game that allows for ‘partial agreements’ and ‘bilateral negotiations’. The solution to these bilateral negotiations is influenced by the outside option of going to the ‘contested garment’ court (recommended in the Talmud for bilateral problems). When the surplus to share is negative (bankruptcy), if the proposer is the highest claimant, the unique subgame perfect equilibrium (SPE) outcome is the nucleolus. If it is someone else, multiplicity of SPE outcomes might arise. When the surplus is positive, the prenucleolus is always obtained as the unique SPE outcome of the game.

A comment on the Nash program and the theory of implementation

The mechanisms in the Nash program for cooperative games are made compatible with the framework of the theory of implementation. This is done through a reinterpretation of the characteristic function that avoids feasibility problems, thereby allowing an analysis that focuses exclusively on the payoff space. In this framework, we show that the core is the only major cooperative solution that is Maskin monotonic. Thus, implementation of most cooperative solutions must rely on refinements of the Nash equilibrium concept (like most papers in the Nash program do). Finally, the mechanisms in the Nash program are adapted into the model.